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Question Number 120529 by bemath last updated on 01/Nov/20

Commented by bemath last updated on 01/Nov/20

Answered by Dwaipayan Shikari last updated on 01/Nov/20

S=1+2a+3a^2 +4a^3 +.....+na^(n−1) −aS= −a−2a^2 −3a^3 −......(n−1)a^(n−1) −na^n S(1−a)=1+a+a^2 +a^3 +...a^(n−1) −na^n S(1−a)=((1−a^n )/(1−a))−na^n S=((1−a^n )/((1−a)^2 ))−na^n =((na^n )/(a−1))−((a^n −1)/((a−1)^2 )) n=50 S=50.2^(50) −2^(50) +1=49.2^(50) +1

S=1+2a+3a2+4a3+.....+nan−1−aS=−a−2a2−3a3−......(n−1)an−1−nanS(1−a)=1+a+a2+a3+...an−1−nanS(1−a)=1−an1−a−nanS=1−an(1−a)2−nan=nana−1−an−1(a−1)2n=50S=50.250−250+1=49.250+1

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